 | Euclides - 1864 - 448 sider
...the remainder BG; (ax. 3.) but it has been shewn that BC is equal to BG, wherefore AL and B Care each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
 | Euclides - 1864 - 262 sider
...the remainder BG ; (ax. 3.) but it has been shewn that BCis equal to BG, wherefore AL and .BCare each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
 | Francis Bacon - 1864 - 528 sider
...whereas in distributive, if unequals be not given to unequals there is the greatest injustice.1 Again " things that are equal to the same are equal to one another," is likewise a rule of mathematics ; but it is at the same time so potent in logic as to be the basis... | |
 | Euclides - 1865 - 402 sider
...the same thing are equal to one another ; therefore tne straight line AI. is equal to BC. (ax. 1.) Wherefore from the given point A a straight line AL...has been drawn equal to the given straight line BC. Which was to be done. PROP. III.— PROBLEM. From the greater of two given straight lines to cut off... | |
 | Robert Potts - 1865 - 528 sider
...the remainder BG; (ax. 8.) but it has been shewn that BC is equal to BG, wherefore AL and BC are each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
 | Sir William Hamilton - 1866 - 548 sider
...certainly than through demonstration, that we know in a common notion.' .... Such common notions are—' Things that are equal to the same are equal to one another,'—' If equals be taken from equals the remainders are equal,'—' Every thing must be either affirmed or... | |
 | Euclid, Isaac Todhunter - 1867 - 424 sider
...to BG. But things which are equal to the same thing are equal to one another. [Axiom 1 . Therefore AL is equal to BC. "Wherefore from, the given point...has been drawn equal to the given straight line BC. QEF PROPOSITION 3. PROBLEM. From the greater of two given straight lines to cut off a part equal to... | |
 | Euclid, Isaac Todhunter - 1867 - 426 sider
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to BC. Wherefore from the given point A a straight line AI, has been drawn equal to the given straight line BC. QEP PROPOSITION 3. PROBLEM. From the greater... | |
 | Robert Potts - 1868 - 434 sider
...the remainder BG; (ax. 3.) but it has been shewn that .BCis equal to BG, wherefore AL and BCaie each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore... | |
 | Euclid, Charles Peter Mason - 1872 - 216 sider
...straight line, the adjacent £s so formed are together equal to two right £s. (Prop. XIII.) 2. That things that are equal to the same are equal to one another. (Ax. I.) 3. That if the same quantity be taken from two equal quantities the remainders are equal.... | |
| |
BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC. 
